Contents

Part - I

Foreword

Preface

1. Relations And Functions

1. Introduction

2. Types Of Relations

3. Types Of Functions

4. Composition Of Functions And Invertible Function

5. Binary Operations

2. Inverse Trigonometric Functions

1. Introduction

2. Basic Conepts

3. Properties Of Inverse Trigonometric Functions

Matrices

1. Introduction

2. Matrix

3. Types Of Matrices

4. Operations On Matrices

5. Transpose Of A Matrix

6. Symmetric And Skew Symmetric Matrices

7. Elementary Operation Of A Matrix

8. Invertible Matrices

Determinants

1. Introduction

2. Determinant

3. Properties Of Determinants

4. Area Of A Triangle

5. Minors And Cofactors

6. Adjoint And Inverse Of A Matrix

7. Application Of Determinants And Matrices

5. Continuity And Differentiabillity

1. Introduction

2. Continuity

3. Differentiability

4. Exponential And Logarithmic Functions

5. Logarithmic Differentiation

6. Derivatives Of Functions In Parametric Forms

7. Second Order Derivative

8. Mean Value Theorem

Application Of Derivatives

1. Introduction

2. Rate Of Change Of Quantities

3. Increasing And Decreasing Functions

4. Tangents And Normals

5. Approximations

6. Maxima And Minima

Appendix 1 Proofs In Mathematics

A 1 Introduction

A 2 What Is A Proof

Appendix 2 Mathematical Modelling

A 1 Introduction

A 2 Why Mathematical Modelling

A 3 Principles Of Mathematical Modelling